Finite Group Databasebeta

← #779098

Subgroups — #779098

Order 512.

5074 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#547C211yesmaximal, characteristic
2C2×#2426C211yesmaximal, characteristic, complemented
3C2×#2451C211yesmaximal, characteristic, complemented
4C2×#2360C211yesmaximal, characteristic, complemented
5#16257C212yesmaximal, complemented
6#15985C212yesmaximal, complemented
7#15983C212yesmaximal, complemented
8#15276C212yesmaximal, complemented
9#15271C212yesmaximal, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15177C211yesmaximal, characteristic, complemented
12#15126C211yesmaximal, characteristic, complemented
13#14964C212yesmaximal, complemented
14#14889C212yesmaximal, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14130C211yesmaximal, characteristic, complemented
17#14053C211yesmaximal, characteristic, complemented
18#14027C211yesmaximal, characteristic, complemented
19#14018C211yesmaximal, characteristic, complemented
20#13998C211yesmaximal, characteristic, complemented
21#13937C212yesmaximal, complemented
22#13907C211yesmaximal, characteristic, complemented
23C4×#394C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25C2×#547—28no—
26C2×#547—28no—
27C2×#547—28no—
28C22×C4⋊Q8C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#123C2212yes—
31C22×#123C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2212yes—
34C22×C22⋊Q8C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×#121C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42#2451—28no—
43#2426—28no—
44C2×#398C2212yes—
45C2×#396C2212yes—
46C2×#395C2212yes—
47C2×#394C2211yescharacteristic
48C2×#394C2212yes—
49C2×#394C2212yes—
50#2360—28no—
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2212yes—
55C2×#391C2212yes—
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2212yes—
59C2×#390C2211yescharacteristic
60C2×#390C2212yes—
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#389C2212yes—
66C2×#388C2212yes—
67C2×#387C2212yes—
68C2×#387C2212yes—
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#385C2212yes—
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2212yes—
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82#1446C2212yes—
83#1444C2212yes—
84#1444C2212yes—
85#1442C2211yescharacteristic
86#1442C2212yes—
87#1441C2211yescharacteristic
88#1441C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1440C2212yes—
94#1440C2211yescharacteristic
95#1440C2211yescharacteristic
96#1440C2212yes—
97#1440C2212yes—
98#1439C2212yes—
99#1439C2211yescharacteristic
100#1439C2211yescharacteristic
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1438C2212yes—
109#1438C2211yescharacteristic
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1437C2212yes—
115#1436C2212yes—
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C4×#95C2211yescharacteristic
129C22×#41—28no—
130C22×#41—28no—
131C22×#41—28no—
132C22×#41—28no—
133C22×#41—44no—
134C22×#41—44no—
135C22×#41—44no—
136C23×Q8C2311yescharacteristic
137C23×Q8C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2312yes—
146C24×C4C2312yes—
147#547—2128no—
148C2×C4⋊Q8—24no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8D418yes—
151C2×#124—24no—
152C2×#124—24no—
153C2×#124—42no—
154C2×#123—28no—
155C2×#123—28no—
156C2×#123—28no—
157C2×#123—28no—
158C2×#123—28no—
159C2×#123—28no—
160C2×C22⋊Q8—28no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—28no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—28no—
168C2×C22⋊Q8—42no—
169C2×#121—24no—
170C2×#121—24no—
171C2×#121—24no—
172C2×#121—24no—
173C2×#121—24no—
174C2×#121D418yes—
175C2×C4×Q8—24no—
176C2×C4×Q8—24no—
177C2×C4×Q8—24no—
178C2×C4×D4—24no—
179C2×C4×D4—24no—
180C2×C4×D4—24no—
181C2×C4×D4—24no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C22×C4⋊C4—24no—
185C22×C4⋊C4—24no—
186C22×C4⋊C4—24no—
187C22×C4⋊C4—24no—
188C22×C4⋊C4—24no—
189C22×C4⋊C4D418yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2312yes—
241#398—28no—
242#396—28no—
243#395—28no—
244#394—28no—
245#394—24no—
246#394—44no—
247#391—28no—
248#391—24no—
249#391—24no—
250#391—24no—
251#391—44no—
252#390—24no—
253#390—28no—
254#390—24no—
255#390—42no—
256#390—44no—
257#389—24no—
258#389—28no—
259#389—24no—
260#389—24no—
261#389—24no—
262#388—28no—
263#387—28no—
264#387—28no—
265#385—28no—
266#385—44no—
267#385—44no—
268#380—24no—
269#380—44no—
270#380—42no—
271C4×C4⋊C4—24no—
272C4×C4⋊C4—24no—
273C4×C22⋊C4—24no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—42no—
277C4×C22⋊C4—42no—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2312yes—
315C25C2412yes—
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C2×#41—264no—
319C2×#41—432no—
320C2×#41—432no—
321C2×#41—432no—
322C2×#41—432no—
323C2×#41—432no—
324C2×#41—432no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—24no—
330C22×Q8—22no—
331C22×Q8—24no—
332C22×Q8—22no—
333C22×Q8—24no—
334C22×Q8—22no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C2×D418yes—
338C22×Q8#4114yescomplemented
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4C2×D414yes—
365C22×D4C2×D418yes—
366C22×D4#4114yes—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2×D414yes—
401C23×C4C2×D418yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C4⋊Q8—232no—
423#124—416no—
424#123—264no—
425#123—264no—
426C22⋊Q8—232no—
427C22⋊Q8—264no—
428C22⋊Q8—416no—
429#121—232no—
430#121—232no—
431C4×Q8—416no—
432C4×D4—232no—
433C4×D4—232no—
434C2×C4⋊C4—232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—232no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4C2×D414yes—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D418yes—
488C2×C4⋊C4C2×D418yes—
489C2×C4⋊C4C2×D414yes—
490C2×C4⋊C4C2×D414yes—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4#4114yescomplemented
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4C2×D418yes—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—24no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—24no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42C2×D414yes—
589#95—22no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—24no—
594#95—22no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—42no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24C22×D414yes—
665C24C22×D412yes—
666C24C22×D412yes—
667C24C2×#4112yes—
668C24C2×#4112yes—
669C24H(5,𝔽2)12yes—
670C24H(5,𝔽2)12yes—
671C24C2511yescharacteristic
672#41—4256no—
673C2×Q8—216no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—216no—
677C2×Q8—28no—
678C2×Q8—48no—
679C2×Q8—48no—
680C2×Q8—48no—
681C2×Q8—48no—
682C2×Q8—48no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—216no—
694C2×D4—216no—
695C2×D4—28no—
696C2×D4—216no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—216no—
724C22×C4—216no—
725C22×C4—216no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—216no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4C22×D412yes—
868C22×C4C22×D414yes—
869C22×C4C22×D414yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D414yes—
873C22×C4C22×D414yes—
874C22×C4C22×D414yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C2×#4114yes—
880C22×C4C2×#4114yes—
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4H(5,𝔽2)12yes—
885C22×C4H(5,𝔽2)12yes—
886C22×C42−1+412yes—
887C22×C42−1+412yes—
888C22×C42−1+412yes—
889C22×C42−1+412yes—
890C4⋊C4—28no—
891C4⋊C4—216no—
892C4⋊C4—28no—
893C4⋊C4—216no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—216no—
897C4⋊C4—216no—
898C4⋊C4—28no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C4⋊C4#120116yes—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C42—28no—
935C42—48no—
936C42—44no—
937C42—44no—
938C42—44no—
939C42—44no—
940C42—84no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23#54614yes—
1045C23#54614yes—
1046C23C23×D411yescharacteristic
1047C23C23×D411yescharacteristic
1048C23C23×D411yescharacteristic
1049C23C22×#4111yescharacteristic
1050C23C22×#4111yescharacteristic
1051C23C22×#4111yescharacteristic
1052C23C2×H(5,𝔽2)11yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×2−1+411yescharacteristic
1057C23C2×2−1+411yescharacteristic
1058C23C2×2−1+411yescharacteristic
1059C23C2×2−1+411yescharacteristic
1060C23#58511yescharacteristic
1061Q8—432no—
1062Q8—416no—
1063D4—232no—
1064D4—432no—
1065D4—432no—
1066D4—416no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—432no—
1110C2×C4—432no—
1111C2×C4—432no—
1112C2×C4—41no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—41no—
1203C2×C4C2×#12018yes—
1204C2×C4C2×#12014yes—
1205C2×C4#52514yes—
1206C2×C4#53714yes—
1207C2×C4#54614yes—
1208C2×C4#54614yes—
1209C2×C4#54714yes—
1210C2×C4#54814yes—
1211C2×C4#55014yes—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22C22×#12011yescharacteristic
1258C22C2×#52511yescharacteristic
1259C22C2×#53711yescharacteristic
1260C22C2×#54611yescharacteristic
1261C22C2×#54611yescharacteristic
1262C22C2×#54611yescharacteristic
1263C22C2×#54611yescharacteristic
1264C22C2×#54711yescharacteristic
1265C22C2×#54811yescharacteristic
1266C22C2×#55011yescharacteristic
1267C22#348211yescharacteristic
1268C22#348211yescharacteristic
1269C22#348411yescharacteristic
1270C22#348411yescharacteristic
1271C22#348411yescharacteristic
1272C22#348611yescharacteristic
1273C22#348611yescharacteristic
1274C22#348911yescharacteristic
1275C22#349711yescharacteristic
1276C22#349711yescharacteristic
1277C22#349911yescharacteristic
1278C22#351311yescharacteristic
1279C22#351511yescharacteristic
1280C22#351711yescharacteristic
1281C22#352011yescharacteristic
1282C22#352011yescharacteristic
1283C22#352211yescharacteristic
1284C22#352211yescharacteristic
1285C22#352211yescharacteristic
1286C22#353611yescharacteristic
1287C22#354211yescharacteristic
1288C22#354411yescharacteristic
1289C22#354411yescharacteristic
1290C22#354811yescharacteristic
1291C22#355211yescharacteristic
1292C4—24no—
1293C4—28no—
1294C4—44no—
1295C4—44no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—82no—
1309C4—81no—
1310C4—82no—
1311C4#240718yes—
1312C2—44no—
1313C2—44no—
1314C2—84no—
1315C2C2×#240711yescharacteristic
1316C2#3568711yescharacteristic
1317C2#3571511yescharacteristic
1318C2#3615211yescharacteristic
1319C2#3642211yescharacteristic
1320C2#3895011yescharacteristic
1321C2#4247711yescharacteristic
1322C2#4487511yescharacteristic
1323C2#4488211yescharacteristic
1324C2#4493011yescharacteristic
1325C2#4493711yescharacteristic
1326C2#5903111yescharacteristic
1327C2#5904011yescharacteristic
1328C2#5940911yescharacteristic
1329C2#5941811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#547C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2426C2semidirect
3. C2×#2451C2semidirect
4. C2×#2360C2semidirect
5. #16257C2semidirect
6. #15985C2semidirect
7. #15983C2semidirect
8. #15276C2semidirect
9. #15271C2semidirect
10. #15215C2semidirect
11. #15177C2semidirect
12. #15126C2semidirect
13. #14964C2semidirect
14. #14889C2semidirect
15. #14139C2semidirect
16. #14130C2semidirect
17. #14053C2semidirect
18. #14027C2semidirect
19. #14018C2semidirect
20. #13998C2semidirect
21. #13937C2semidirect
22. #13907C2semidirect
23. C4×#394C2semidirect
338. C22×Q8#41semidirect
492. C2×C4⋊C4#41semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#5472
C2×#24262
C2×#24512
C2×#23602
#162572
#159852
#159832
#152762
#152712
#152152
#151772
#151262
#149642
#148892
#141392
#141302
#140532
#140272
#140182
#139982
#139372
#139072
C4×#3942